Color banding in Blender Internal render output
I am very appreciative of information found on blendhelp.com... (Has the site died?)
https://www.youtube.com/watch?v=YwrTaXXSZsY

In any case, the solution to my banding involved:

** Select PNG output and 16-bit color depth

** In post-processing, select an appropriate dither amount. I worked between 1 and 2 and seem to get a nice smooth transition.

This explains why I did not see it earlier, as the original color range was probably narrow enough not to generate this banding.

Hope this helps someone in the future!

Please note all input from troy_s below, as these are really helping me dial this in. PNGs did not work as well as Targas, which do not seem to work as well as EXRs.